Page Th e’s a science to it! - Fractal Science and Math ... · PDF fileTh!e’s a science to it! ... Written by Montclair High School Math Teacher Ryan Casazza ... Let = area of

Page �1

There’s a science to it!

FractalAcademy.com [email protected] Call or Text 862-500-1101

REDESIGNED SAT Practice Material Written by Montclair High School Math Teacher Ryan Casazza

Topic: Geometry and Statistics *All answers are at the end of this document.

1) Rectangle ABCD below has diagonals AC and BD intersecting at E.

Let = area of triangle AEC and let = area of triangle CED. Which of the following statements is

true?

2) Consider the following scatterplot:

!

Which of the following coordinates, when added to this data, would most weaken the correlation?

!x !y

!!

A) x > yB) y < xC) x = yD) cannot bedetermined from the information given

0

4

7

11

14

0 8 15 23 30

!!

A) 0, 17( )B) 15,2( )C) 20,6( )D) 40,0( )


A B

C D

E

http://FractalAcademy.com

mailto:[email protected]



Page �2

Use the information below to answer questions 3 and 4

The table below shows the number of registered voters in a city planning to vote for candidates A, B, or C. The city has been sectioned into four parts: North, South, East, and West. Use this table for the next 2 questions

3) Which of the following statements is definitely FALSE, based on the table?

A) Candidate B currently has more voters planning to vote for him/her than either of the other 2 candidates

B) Approximately 50% of the voters in the East section plan to vote for candidate B C) The ratio of voters in the North section planning to vote for candidate A to NOT voting for candidate

A is approximately 1:4 D) Of all 4 sections, the South section has the highest percent of its voters planning to vote for

candidate B

4) Suppose x new voters were polled in the North section such that the ratio of candidate B voters to non-candidate B voters was 1:1. What is the least possible value for x?

Region

North South East West

Candidate A 24 108 48 59

Candidate B 73 121 53 100

Candidate C 19 53 6 25

!!

A) 15B) 30C) 49D) 54




Page �3

5) In the triangle at right, . Which of the following

MUST be true?

6)

Note: Figure not drawn to scale

Two isosceles triangles share a common segment, as shown above. If , and , then what is the

value of x?

!!cosx > cos y

!!

A) x > yB) y > xC) x = yD) cannot bedetermined from theinformation given

!!w =100° !y = z

!!

A) 40°B) 50°C) 60°D) 70°


x°

y°

w°

z°

x°

y°



Page �4

7)

At Nuni Underwriters’ New Instruction School (NUNIS), the number of students who made Honor Roll or High Honor Roll are separated by grade and listed above. If a student either on Honor Roll or High Honor Roll is chosen at random, what is the approximate probability that he/she is not a senior?

8) If and , then what is the value of ?

9) A basketball team has played eight games. The average (arithmetic mean) number of points they have earned is 88. What is the minimum number of they must score on the next game to have an average of at least 90?

!!

A) 39%B) 55%C) 61%D) 69%

!!sin x°( )= cos 2x°( ) !!0< x <180 !!3x

!!

A) 30°B) 60°C) 90°D) 120°




Page �5

10) The table above is incomplete. It displays the timing of teachers’ and students’ birthdays (either during the school year or not) for a particular school. Three times as many teachers have birthdays during the school year than not during the school year, and the ratio of students with school year birthdays to non-school year birthdays is 4:1. If a person with a school-year birthday is chosen at random, which of the following is the closest to the probability that he/she is a teacher?

11) A circle in the xy-plane has equation . Which of the following is NOT true regarding this

circle?

A) Its center is located at

B) It has a diameter of

C) It passes through the coordinate

D) It does not intersect the line

!!

A) 0.087B) 0.095C) 0.102D) 0.113

!!x2 + y+9( )2 = 14

! 0,−9( )

!14

!0, 81

2!

"#$

%&

!y = x




Page �6

12)


In the diagram above, lines p and q are parallel. Lines m, n, and q all intersect at point A. If the measure of and the measure of , then what is the measure of ?

!∠1=100° !∠2=65° !∠3

!!

A) 35°B) 45°C) 55°D) 65°


n m

p

q2

1 3

A



Page �7Questions 13 and 14 refer to the following information

Sharkeisha interviews her 14 classmates to find out the number of siblings each student has. She presented her findings in a frequency chart, as seen above

13) Which of the following is closest to the average (arithmetic mean) number of siblings in Sharkeisha’s class?

14) If x = the median value of number of siblings and y = the mode value of number of siblings, then which of the following is true?

!!

A) 2B) 3C) 4D) 5

!!

A) x = yB) x > yC) x < yD) cannot bedetermined!from theinformation given


Number of SiblingsFr

eq

uen

cy

0

1

3

4

5

Number of Siblings



Page �8

15)

The cone above has volume of cubic feet. What is the circumference of the base of the cone, in

feet?

16)


In the figure above, and segment intersects segment at E. What is the length of AD?

!

!8π

!!

A) 2πB) 4πC) 6πD) 8π

!AD !CB

!!

A) 9B) 15C) 16D) 22


6 cm

A

B

C

D

E

12

8

6



Page �9 17)


In the xy-plane above, O is the center of a circle and point Z lies in quadrant I. If and the measure of is equal to radians, then which of the following could NOT be a value for n?

18) A spherical dome with volume V covers a plate with radius r. The volume of the dome can be found by using the formula . Another spherical dome has volume 8 times that of the original dome. How many

times larger is the radius of the new dome compared to the original dome?

!

!b<a!∠YOZ

!π

n

!!

I . n=3II . n= 4III . n=5

!!

A) I onlyB) I and II onlyC) II and III onlyD) III only

!!V = 2

3πr 3

!!

A) 2B) 8C) 64D) 128


!O!x

!y

!! a,b( )

!Y

!Z



Page �10

19) In order to determine if FluKiller Medication is successful in the treatment of flu symptoms, a research study was conducted. From a large population of people who currently had the flu, 80 participants were selected at random. Half of the participants were given FluKiller and the other half were not. The resulting data showed that the participants who were given FluKiller were able to combat the flu in half the time it took the other half who were not given FluKiller. Based on the design and results of the study, which of the following is an appropriate conclusion?

A) FluKiller is the best mediation available at combating flu symptoms B) Taking FluKiller will prevent people from ever getting the flu C) FluKiller will lessen the time it takes to combat the flu D) Anyone who takes FluKiller will have the flu for a short time

20) In circle O, with minor arc AB, the area of sector AOB is the area of the entire circle. What is the

radian measure of central angle AOB?

!512

!!

A) 5π6

B) 5π12

C) 5π24

D) 5π36




Page �1121)

What proportion of injuries involve concussions from Football and Soccer?

!!

A) 38

B) 2564

C) 78

D) 2425




Page �12Use the following information for questions 22 and 23

The bar graph above shows the number of complaints each year a local car dealership has received on behalf of two different cars—car A and car B

22) In 2016 the number of complaints for car A is x, and the average (arithmetic mean) number of complaints from 2010-2016 is now 9. What is the value of x?

! 23) The average rate of change of complaints per year from 2010 to 2012 for car A is the same as the average rate of change for which time interval for car B?

!

!!

A) 0B) 4C) 7D) 10

!!

A) 2011 to 2012B) 2012 to 2014C) 2013 to 2015D) 2011 to 2015




Page �1324)

The table above shows the scores for all of Nuni’s assignments this quarter. Her teacher has promised that he will drop the lowest score. Of the mean, median, and range values, which will be most affected if the lowest score is removed from the data?

A) Mean B) Median C) Range D) They will all change by the same amount.

Use the following information to answer questions 25 and 26

A researcher is interested in knowing how the people in her town plan to spend their summer. She visits the community pool and interviews 50 random people regarding their summer plans. Her results are below

25) What is the probability that a person chosen at random planned on going to the beach, given that they actually did not refuse to answer?

!

26) Which of the following factors makes it least likely that a reliable conclusion can be drawn regarding the summer plans for all the people in the researcher’s town?

A) The sample size B) The number of people who refused to answer C) Where the survey was taken D) The number of people who answered ‘other’

!!

A) 32.0%B) 35.6%C) 42.0%D) 47.8%




Page �14

27) In the circle below, two chords intersect. Each chord is divided into two smaller segments with integer lengths a, b, c, and d as shown above. Assume ! . If ! , ! , and ! , then which of the following is the largest possible value for a?

!

28) A local college posts that the average math SAT score of its attendees is 520 and the median SAT score is 580. Which of the following could explain the difference between the mean and median SAT scores?

A) Almost all attendees of the college got scores between 520 and 580 B) There are a few SAT scores that are much lower than the rest C) There are a few SAT scores that are much higher than the rest D) An unusually high percentage of students got 550 for their score

29)

The data in the table above show the results of an exercise study. One hundred and fifty runners were selected to be in the study. Group A consisted of 50 people chosen at random during the winter, group B were 50 people studied during the spring, and group C was comprised of 50 people chosen during the summer. For each participant, the average number of miles run per week was recorded. Assuming a runner chosen at random ran 10 or less miles, what is the probability that he/she was a member of group B?

!

!ac= db !!d = 9 !!b=16 !c>b

!!

A) 4B) 6C) 8D) 12

!!

A) 950

B) 41107

C) 107200

D) 943


a b

cd



Page �15

30) Three lines, m, n, and p, intersect and create six angles as shown. If ! and ! , then what is the value of c?

31) The toy top above is a right cylinder fused with a right cone, each with equal height. The diameter of the cylinder is equal to its height. If the height of the entire toy is x inches, what is the volume of the toy in terms of x?

!

!a= b !!f =3a−b

!!

A) 3πx3

16

B) πx3

24

C) πx3

64

D) 3πx3

128


mn

pa° b°c°d°e°

f°


x in



Page �16

32) Two circles have equations of ! and ! where a is a positive integer. What is the maximum value for a such that the two circles do not intersect?

33) In the diagram above, lines m and an are parallel. If ! , then which of the following is true about y?

!

34) The center of a circle is at the origin of a rectangular coordinate plane. If the points ! , ! !

and ! are on the circumference of the circle, what is the probability that a randomly selected point from within the circle will fall within the quadrilateral formed by those three points?

!

!!x2 + y−7( )2 =16 !! x+7( )2 + y−7( )2 = a

!!x <90

!!

A) y <90B) y = 90C) y >90D) Cannot bedetermined

! −4,0( ) ! 0,−4( )! 0,4( )

! 4,0( )

!!

A) 12

B) 2π

C) 3π4

D) 3π


m

n

p

x°

y°




Page �17

35) In the figure above, circle O is tangent to the x-axis at point A and to the y-axis at point B. If ! and ! , then what is the area of circle O?

!

!!CD=2⋅DA!!AC=1

!!

A) π

5

B) π

3

C) π 33

D) π 55


A

B

C

O

D x

y



Page �18

36)

In the figure above, lines c and d are parallel, and lines a and b are parallel. If the measure of ! is ! , what is the measure of ! ?

37)

The number of trees taken down by a particular company is shown in the graph above. If the average number of trees taken down during this period is 210, what is appropriate label for the vertical axis of the graph?

A) Number of trees taken down B) Number of trees taken down (in tens) C) Number of trees taken down (in hundreds) D) Number of trees taken down (in thousands)

!∠1 !67°!∠2


a b

c

d1

2

Number of Trees Removed

0

10

20

30

40

Jan Feb Mar Apr May



Page �1938) An old rectangular painting measures 8 feet by 6 feet. Eight art historians each mark off a randomly selected region of the painting; each region is a square and has side lengths of ½ feet, and no two regions overlap. The historians look for the number of ancient symbols written small in their sections. Their results are shown below

Which of the following is a reasonable approximation of the number of ancient symbols written in the entire painting?

!

39)

According to the line of best fit in the scatterplot above, which of the following best approximates the year in which the number of identified stars in the universe was estimated to be 45 million?

!

!!

A) 9B) 90C) 900D) 9,000

!!

A) 1985B) 1990C) 1995D) 2000


Number of Identified Stars in the Universe

Ob

serv

ed

S

tars

(M

illio

ns)

0

15

30

45

60

Year

1950 1963 1975 1988 2000



Page �20

40)

The figure above shows a square with sides of length of n and an equilateral triangle with sides of length n. If

the area of the triangle is ! square centimeters, then what is the area, in square centimeters of the square?

!

41)

In the figure above, point O is the center of the circle, line segments AC and BC are tangent to the circle at points A and B respectively, and the segments intersect at point C as shown. If ! and the area of circle

O is ! , then what is the length of minor arc ! ?

42) In triangle XYZ, the measure of ! , YZ = 30 and XZ = 34. Triangle ABC is similar to triangle XYZ, where vertices A, B, and C correspond to vertices X, Y, and Z, respectively, and each side of triangle

ABC is ! the length of the corresponding side of triangle XYZ. What is the value of ! ?

!

!9 3

!!

A) 9B) 16C) 36D) 81

!!∠C=30°

!36π

!!∠Y= 90°

!67 !!cosC

!!

A) 815

B) 158

C) 817

D) 1517


O

A

B

C



Page �21

43) Millie took 19 tests over the course of a year. She recorded how many hours she studied for the test and her resultant score. The scatterplot above shows her results, along with the line of best fit for the data. For the test that she studied three hours, Millie’s score was how much below the score predicted by the line of best fit?

!

44) In a circle with center O, central angle XOY has a measure of ! radians. The ratio of sector XOY’s area to the area of the circle NOT enclosed by sector XOY is r:1. What is the value of r?

!!

A) 4B) 8C) 12D) 16

!7π6


Score on test versus hours studied

Sco

re

50

63

75

88

100

Hours Studied

0 1.3 2.5 3.8 5

3

5

4



Page �2245) Carlotita has a bookshelf in the shape of a trapezoid. She wishes to place books on the bottom ledge. If the entire bookshelf is 30 inches tall, then what is the tallest book that she can place on the bottom ledge?

!

46) Circle O has minor arc AB that is 10 units long. If ! is between 120 and 150 degrees, and the diameter of circle O is an integer, what is one possible value of the diameter of circle O?

47) Circle O has center at the origin of the xy-coordinate plane. If circle O has area of ! , then which of the following points does NOT lie on the circumference of circle O?

!

!!

A) 10 inchesB) 12 inchesC) 15 inchesD) 20 inches

!m∠AOB

!100π

!!

A) 10,0( )B) 6,−8( )C) 8,−6( )D) 5,−5( )




Page �23

ANSWER KEY: 1. C 2. B 3. D 4. B 5. B 6. D 7. C 8. C 9. 106 10. A 11. B 12. A 13. B 14. B 15. B 16. B 17. A 18. A 19. C 20. A 21. A 22. B 23. A 24. C 25. B 26. C 27. C 28. B 29. B 30. 90 31. B 32. 8 33. C 34. B 35. A 36. 113 37. B 38. C




Page �2439. C 40. C 41. 5pi 42. D 43. B 44. 7/3 45. A 46. 8 or 9 47. D




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Page Th e’s a science to it! - Fractal Science and Math ... · PDF fileTh!e’s a science to it! ... Written by Montclair High School Math Teacher Ryan Casazza ... Let = area of